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A linear programming computer package is needed. The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows. Type of Loan/Investment Annual Rate of Return (%) Automobile loans Furniture loans 11 Other secured loans 12 Signature loans 13 Risk-free securities 10 The credit union will have $2,400,000 available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments. • Risk-free securities may not exceed 30% of the total funds available for investment. Signature loans may not exceed 10% of the funds invested in all loans (automobile, furniture, other secured, and signature loans). Furniture loans plus other secured loans may not exceed the automobile loans. • Other secured loans plus signature loans may not exceed the funds invested in risk-free securities. How should the $2,400,000 be allocated to each of the loan/investment alternatives to maximize total annual return? Automobile loans Furniture loans Other secured loans $4 Signature loans Risk-free securities What is the projected total annual return?

A linear programming computer package is needed. The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows. Type of Loan/Investment Annual Rate of Return (%) Automobile loans Furniture loans 11 Other secured loans 12 Signature loans 13 Risk-free securities 10 The credit union will have $2,400,000 available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments. • Risk-free securities may not exceed 30% of the total funds available for investment. Signature loans may not exceed 10% of the funds invested in all loans (automobile, furniture, other secured, and signature loans). Furniture loans plus other secured loans may not exceed the automobile loans. • Other secured loans plus signature loans may not exceed the funds invested in risk-free securities. How should the $2,400,000 be allocated to each of the loan/investment alternatives to maximize total annual return? Automobile loans Furniture loans Other secured loans $4 Signature loans Risk-free securities What is the projected total annual return?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section4.7: Financial Models
Problem 38P
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A linear programming computer package is needed. The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows. Type of Loan/Investment Annual Rate of Return (%) Automobile loans 9. Furniture loans 11 Other secured loans 12 Signature loans 13 Risk-free securities 10 The credit union will have $2,400,000 available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments. • Risk-free securities may not exceed 30% of the total funds available for investment. Signature loans may not exceed 10% of the funds invested in all loans (automobile, furniture, other secured, and signature loans). • Furniture loans plus other secured loans may not exceed the automobile loans. • Other secured loans plus signature loans may not exceed the funds invested in risk-free securities. How should the $2,400,000 be allocated to each of the loan/investment alternatives to maximize total annual return? Automobile loans $ Furniture loans 2$ Other secured loans Signature loans Risk-free securities 2$ What is the projected total annual return? $ %24
Transcribed Image Text:A linear programming computer package is needed. The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows. Type of Loan/Investment Annual Rate of Return (%) Automobile loans 9. Furniture loans 11 Other secured loans 12 Signature loans 13 Risk-free securities 10 The credit union will have $2,400,000 available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments. • Risk-free securities may not exceed 30% of the total funds available for investment. Signature loans may not exceed 10% of the funds invested in all loans (automobile, furniture, other secured, and signature loans). • Furniture loans plus other secured loans may not exceed the automobile loans. • Other secured loans plus signature loans may not exceed the funds invested in risk-free securities. How should the $2,400,000 be allocated to each of the loan/investment alternatives to maximize total annual return? Automobile loans $ Furniture loans 2$ Other secured loans Signature loans Risk-free securities 2$ What is the projected total annual return? $ %24
Expert Solution
Step 1: Variables

A = Amount to be allocated to Automobile loan

F  = Amount to be allocated to Furniture loan

O = Amount to be allocated to Other secured loans

S = Amount to be allocated to Signature loan

R = Amount to be allocated to Risk-free securities

 

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